Which of the following is a prime number ?

Options

A. 81
B. 87
C. 91
D. 97

Answer

To determine which of the following numbers is a prime number, we will analyze each number based on the definition of prime numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

**Step 1: Analyze the first number, 81.**
- Factors of 81: 81 can be factored as 3 x 3 x 3 x 3 (or 3^4).
- Since 81 has factors other than 1 and itself (specifically, it can be divided by 3), it is not a prime number.

**Step 2: Analyze the second number, 87.**
- Factors of 87: 87 can be factored as 1 x 3 x 29.
- Since 87 has factors other than 1 and itself (it can be divided by 3 and 29), it is not a prime number.

**Step 3: Analyze the third number, 91.**
- Factors of 91: 91 can be factored as 7 x 13.
- Since 91 has factors other than 1 and itself (it can be divided by 7 and 13), it is not a prime number.

**Step 4: Analyze the fourth number, 97.**
- Factors of 97: 97 can only be factored as 1 x 97.
- Since 97 has no factors other than 1 and itself, it is a prime number.

**Conclusion:**
The only prime number among the options is **97**.

---